“High dimensional spatio-temporal modeling with matrix variate distributions”

Dr. Shuheng Zhou, University of Michigan, Ann Arbor

 

Date: Thursday, December 03, 2015

Time: 3:30 PM – 4:30 PM

Location: 269 Everitt

Sponsor: Department of Statistics

 

Abstract:

In the first part of this talk, I will discuss new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from the matrix variate data. Under sparsity conditions, we show that one is able to recover the graphs and covariance matrices with a single random matrix from the matrix variate normal distribution. Our method extends, with suitable adaptation, to the general setting where replicates are available.

 

In the second part of talk, I will discuss an errors-in-variables model where the covariates in the data matrix are contaminated with random noise. Under sparsity and restrictive eigenvalue type of conditions, we show that one is able to recover a sparse vector $\beta \in \mathbb{R}^m$ from the model given a single observation matrix X and the response vector y. This model is significantly different from those analyzed in the literature in the sense that we allow the measurement error for each covariate to be a dependent vector across its n observations. Such error structures appear in the science literature, for example, when modeling the trial-to-trial fluctuations in response strength shared across a set of neurons.

 

We provide a real-data example and simulation evidence showing that we can recover graphical structures as well as estimating the precision matrices and the regression coefficients for these two classes of problems.

 

http://illinois.edu/calendar/detail/1439?eventId=32723391&calMin=201511&cal=20151130&skinId=13335